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A213372 Triangle read by rows in which row n lists the number of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.

%I A213372 #28 Sep 03 2012 07:14:25
%S A213372 2,4,2,6,2,4,8,4,6,2,10,8,6,12,4,2,8,10,14,4,6,2
%N A213372 Triangle read by rows in which row n lists the number of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.
%C A213372 First differs from A212122 at a(14).
%C A213372 The list of the spin-orbit coupling of this version of the nuclear shell model starts: 1s_(1/2), 1p_(3/2), 1p_(1/2), 1d_(5/2), 2s_(1/2), 1d_(3/2), 1f_(7/2), 2p_(3/2), 1f_(5/2), 2p_(1/2), 1g_(9/2), 1g_(7/2), 2d_(5/2), 1h_(11/2), etc. (see link section). The numerators of the fractions are 1, 3, 1, 5, 1, 3, 7, 3, 5, 1, 9, 7, 5, 11,... then we add 1 to every numerator, so we have this sequence: 2, 4, 2, 6, 2, 4, 8, 4, 6, 2, 10, 8, 6, 12,... Other sequences that arise from this sequence are A213371, A213373, A213374. - _Omar E. Pol_, Sep 02 2012
%D A213372 W. E. Meyerhof, Elements of Nuclear Physics (McGraw-Hill, New York, 1967), Chap. 2.
%H A213372 HyperPhysics, G.S.U., <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html">Shell Model of Nucleus</a>
%H A213372 W. E. Meyerhof, <a href="http://www.flickr.com/photos/mitopencourseware/3772864128/in/set-72157621892931990">Energy Levels of Nucleons in a Smoothly-Varying Potential Well</a>, MIT OpenCourseWare
%F A213372 a(n) = 2*A213371(n).
%e A213372 Illustration of initial terms on one of views of a three-dimensional shell model of nucleus.
%e A213372 .
%e A213372 .  |---------------------- i ----------------------|
%e A213372 .  |                                               |
%e A213372 .  |   |------------------ h ------------------|   |
%e A213372 .  |   |                                       |   |
%e A213372 .  |   |   |-------------- g --------------|   |   |
%e A213372 .  |   |   |                               |   |   |
%e A213372 .  |   |   |   |---------- f ----------|   |   |   |
%e A213372 .  |   |   |   |                       |   |   |   |
%e A213372 .  |   |   |   |   |------ d ------|   |   |   |   |
%e A213372 .  |   |   |   |   |               |   |   |   |   |
%e A213372 .  |   |   |   |   |   |-- p --|   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |       |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   s   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   2   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   4   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   |   2   |   |   |   |   |
%e A213372 .  |   |   |   |   6   |   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   2   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   |   |   4   |   |   |   |
%e A213372 .  |   |   |   8   |   |   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   4   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   |   |   |   6   |   |   |
%e A213372 .  |   |   |   |   |   |   |   2   |   |   |   |   |
%e A213372 .  |   |  10   |   |   |   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   |   |   |   |   8   |   |
%e A213372 .  |   |   |   |   6   |   |   |   |   |   |   |   |
%e A213372 .  |  12   |   |   |   |   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   |   |   4   |   |   |   |
%e A213372 .  |   |   |   |   |   |   2   |   |   |   |   |   |
%e A213372 .  |   |   |   8   |   |   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   |   |   |   |   |  10   |
%e A213372 . 14   |   |   |   |   |   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   4   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   |   |   |   6   |   |   |
%e A213372 .  |   |   |   |   |   |   |   2   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   |   |   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |   |1/2|   |   |   |   |   |
%e A213372 .  |   |   |   |   |   |           |   |   |   |   |
%e A213372 .  |   |   |   |   |   |----3/2----|   |   |   |   |
%e A213372 .  |   |   |   |   |                   |   |   |   |
%e A213372 .  |   |   |   |   |--------5/2--------|   |   |   |
%e A213372 .  |   |   |   |                           |   |   |
%e A213372 .  |   |   |   |------------7/2------------|   |   |
%e A213372 .  |   |   |                                   |   |
%e A213372 .  |   |   |----------------9/2----------------|   |
%e A213372 .  |   |                                       |   |
%e A213372 .  |   |-------------------11/2--------------------|
%e A213372 .  |
%e A213372 .  |-----------------------13/2------------------------
%e A213372 .
%e A213372 For another view of the model see the example section of A212122, second part.
%e A213372 Written as an irregular triangle in which row n represents the n-th shell of nucleus. Note that row 4 has only one term. Triangle begins:
%e A213372 2;
%e A213372 4, 2;
%e A213372 6, 2, 4;
%e A213372 8;
%e A213372 4, 6, 2, 10;
%e A213372 8, 6, 12, 4, 2;
%e A213372 8, 10, 14, 4, 6, 2;
%Y A213372 Partial sums give A213374. Other versions are A162630, A212012, A212122, A213362.
%Y A213372 Cf. A213371, A213373.
%K A213372 nonn,tabf,hard,more
%O A213372 1,1
%A A213372 _Omar E. Pol_, Jul 16 2012